MATHEMATICS HIGH SCHOOL

What is the simplified form of the quantity of x plus 5, all over the quantity of 3x plus 4 + the quantity of x plus 4, all over the quantity of x plus 3?

Answers

Answer 1
Answer:

Answer: (4x^2+24x+31)/(3x^2+13x+12)

Step-by-step explanation:

Since the given expression ,

(x+5)/(3x+4) + (x+4)/(x+3)

=((x+5)(x+3)+(x+4)(3x+4))/((3x+4)(x+3)) ( by taking the LCM for solving the fraction)

=(x^2+5x+3x+15+3x^2+12x+4x+16)/(3x^2+9x+4x+12) ( By multiplying)

=(x^2+8x+15+3x^2+16x+16)/(3x^2+13x+12)

=(4x^2+24x+31)/(3x^2+13x+12) ( by adding the like terms)
Answer 2
Answer: (x + 5)/(3x + 4) + (x + 4)/(x + 3) = ((x + 5)(x + 3))/((3x + 4)(x + 3)) + ((x + 4)(3x + 4))/((3x + 4)(x + 3)) = (x(x + 3) + 5(x + 3))/((3x(x + 3) + 4(x + 3)) + (x(3x + 4) + 4(3x + 4))/(3x(x + 3) + 4(x + 3)) = (x(x) + x(3) + 5(x) + 5(3))/(3x(x) + 3x(3) + 4(x) + 4(3)) + (x(3x) + x(4) + 4(3x) + 4(4))/(3x(x) + 3x(3) + 4(x) + 4(3)) = (x^(2) + 3x + 5x + 15)/(3x^(2) + 9x + 4x + 12) + (3x^(2) + 4x + 12x + 16)/(3x^(2) + 9x + 4x + 12) = (x^(2) + 8x + 15)/(3x^(2) + 13x + 12) + (3x^(2) + 16x + 16)/(3x^(2) + 13x + 12) = ((x^(2) + 8x + 15) + (3x^(2) + 16x + 16))/(3x^(2) + 13x + 12) = ((x^(2) + 3x^(2)) + (8x + 16x) + (15 + 16))/(3x^(2) + 13x + 12) = (4x^(2) + 24x + 31)/(3x^(2) + 13x + 12)

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If an 8 pound bag of rice cost $9.60 , what is the cost of 1 pound of rice ?

Answers

the answer is $1.20
to get this you divide 9.60 by 8

3x=25-4




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Answers

Answer:

x = 7

Step-by-step explanation:

The first step to solving this problem is combining like terms.  25 - 4 = 21, so now we have 3x = 21.  To simplify this, we need to divide both sides by the coefficient of x, which is 3 in this case.  3x/3 = 21/3 gives us x = 7.  

What is the range of the function f(x) = -2x + 5 when the domain is {-5, 5}.

Answers

Answer:

{-5,15}

Step-by-step explanation:

because this function is constantly decreasing, we can get our range by looking at the endpoints:

f(-5) = 15

f(5) = -5

Help me factor the trinomial completely

-r^2+6r-9

Answers

-r^2+6r-9 = - ( r^2 - 6r + 9) = - ( r - 3)^2;

A local bowling alley charges $3 per game, plus $5 to rent a pair of shoes. Write an algebraic expression that models the cost of renting one pair shoes and bowling g games.

Answers

Answer:

5+3g

Step-by-step explanation:

This is because you pay $5 for shoes and $3 per game. Since the amount of games is unknown you put g.

Amelia used 19/20 pounds of flour to bake a cake. Write the quantity of flour she used in ____ decimal form. The decimal quantity of the flour Amelia used to bake the cake is pound.

Answers

Answer:

The decimal quantity of the flour Amelia used to bake the cake is 0.95 pound.

Step-by-step explanation:

Amelia used 19/20 pounds of flour to bake a cake.

We have to write the quantity of flour she used in decimal form.

To write in decimal form, we will divide 19 by 20.

So, the decimal quantity of the flour Amelia used to bake the cake is 0.95 pound.
.95 just divide 19/20
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